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Math Help - Integrating factors

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    Integrating factors

    So, some guidance would be helpful.

    ydx+(2xy-e^{-2y})dy = 0<br />

    \frac{1-2y}{-y}

    e^{^-{\int \frac{1}{y}-2}}

    \frac{e^{2y}}{y} is the integrating factor.

    And upon solving, the answer is: C = xe^{2y}-ln|y|?
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    y\,dx + (2xy - e^{-2y})\,dy = 0

    y\,\frac{dx}{dy} + 2xy - e^{-2y} = 0

    \frac{dx}{dy} + 2x - \frac{e^{-2y}}{y} = 0

    \frac{dx}{dy} + 2x = \frac{e^{-2y}}{y}.


    The integrating factor is e^{\int{2\,dy}} = e^{2y}

    So multiplying through by the integrating factor gives

    e^{2y}\,\frac{dx}{dy} + 2e^{2y}x = \frac{1}{y}

    \frac{d}{dy}(e^{2y}x) = \frac{1}{y}

    e^{2y}x = \int{\frac{1}{y}\,dy}

    e^{2y}x = \ln{|y|} + C

    x = e^{-2y}\ln{|y|} + Ce^{-2y}.
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    If I had solved for x at the end, I would've gotten the same answer. Is my integrating factor incorrect?
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    Quote Originally Posted by A Beautiful Mind View Post
    If I had solved for x at the end, I would've gotten the same answer. Is my integrating factor incorrect?
    I don't see how you got your Integrating Factor to be honest...

    But your final answer looks correct.
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    I applied a formula.

    I don't know how to do the subscript things on latex but...

    \frac{My-Nx}{-M}
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